Unlike the BA algorithm and its variants[1]}, we propose a novel framework based on the optimal transport (OT) approach for quantitative measurement of bounds in communication theory, which we name as the Communication Optimal Transport (CommOT).
The OT problem is a famous mathematical problem with long history [2]}.
The proposal of the CommOT framework in the present paper is inspired by the connection between bounds in communication theory and the OT problem.
Specifically, the transition law and relative entropy function in communication theory [3]} are regarded as the transport plan and objective function in the entropy regularized OT problem.
Also, the distributions of the source and reproduction alphabets in the former are viewed as the marginal distribution constraints in the latter.
Recently, GPU acceleration and the Sinkhorn algorithm [4]}, [5]} have greatly boosted the computation of the regularized OT problem, which drives us to consider the application of the OT approach in communication theory.
